Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization

2026-03-24

AI Summary

Achieving conditional coverage in conformal prediction under limited samples is highly challenging due to intractable pointwise constraints. This work proposes the MOPI framework, which reformulates the conditional coverage problem as a minimax optimization task—bypassing the structural limitations of traditional approaches that rely on predefined scoring functions. Instead of using fixed sublevel sets, MOPI flexibly constructs an adaptive set-valued mapping during calibration. By incorporating marginal moment constraints and leveraging non-asymptotic oracle inequalities, the method enables valid conditional inference even for sensitive attributes unseen at test time. Empirical evaluations demonstrate that MOPI substantially outperforms existing methods on complex, non-standard conditional distributions, yielding prediction sets that are both tighter and theoretically optimal in terms of convergence rate.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal moment restrictions, we introduce Minimax Optimization Predictive Inference (MOPI), a framework that generalizes prior work by optimizing over a flexible class of set-valued mappings during the calibration phase, rather than simply calibrating a fixed sublevel set. This minimax formulation effectively circumvents the structural constraints of predefined score functions, achieving superior shape adaptivity while maintaining a principled connection to the minimization of mean squared coverage error. Theoretically, we provide non-asymptotic oracle inequalities and show that the convergence rate of the coverage error attains the optimal order under regular conditions. The MOPI also enables valid inference conditional on sensitive attributes that are available during calibration but unobserved at test time. Empirical results on complex, non-standard conditional distributions demonstrate that MOPI produces more efficient prediction sets than existing baselines.

Problem

• conformal prediction
• conditional coverage
• shape adaptivity
• minimax optimization
• sensitive attributes

Innovation

• conformal prediction
• minimax optimization
• conditional coverage
• shape adaptivity
• set-valued mapping